The figure below shows the graph 6x - 3y = 12
Graphing a linear equation involves the following steps:
Rewrite the equation in slope-intercept form:
6x - 3y = 12
-6x + 6x - 3y = 12 - 6x (Subtract 6x from both sides to isolate y)
-3y = 12 - 6x
y = -4 + 2x (Divide both sides by -3)
Therefore, the equation in slope-intercept form is y = 2x - 4
Identify the slope and y-intercept:
The slope (m) is the coefficient of the x term in the slope-intercept form. In this case, the slope is 2.
The y-intercept (b) is the point where the line crosses the y-axis. In this case, the y-intercept is -4.
Set up the graph:
Create a coordinate plane with x and y axes. Label the x-axis "x" and the y-axis "y". Choose a scale that is appropriate for the values of your equation.
Plot the y-intercept:
The y-intercept is the point where the line crosses the y-axis. In this case, the y-intercept is -4, so place a point on the graph at (0, -4).
Use the slope to find additional points:
The slope tells you rise over run. In this case, the slope is 2, which means that for every 2 positions you move up (because it's positive), you must also move 1 position to the right.
From the y-intercept (0, -4), move up 2 positions and right 1 position to find another point on the line. This point is (1, -2).
Draw the line:
Use a ruler to connect the two points you plotted. The line should pass through both points and extend infinitely in both directions.
Label the graph:
Label the x-axis and y-axis with their respective variables. Write the equation of the line in the top corner of the graph.
Your graph should now show the line representing the equation 6x - 3y = 12.